Many-body quantum chaos in mixtures of multiple species

TL;DR

This paper investigates spectral correlations and chaos in multi-species quantum systems with different mixing types, deriving Hamiltonians and analyzing how spectral properties scale with system size, revealing different chaos regimes.

Contribution

It introduces analytical derivations of Hamiltonians for mixed quantum species and characterizes the system-size scaling of Thouless time under different mixing conditions.

Findings

Thouless time scales as log L to L^2 depending on mixing type.

Jaynes-Cummings mixing leads to L^2 scaling in the thermodynamic limit.

Rabi mixing results in logarithmic scaling of Thouless time.

Abstract

We study spectral correlations in many-body quantum mixtures of fermions, bosons, and qubits with periodically kicked spreading and mixing of species. We take two types of mixing, namely, Jaynes-Cummings and Rabi, respectively, satisfying and breaking the conservation of a total number of species. We analytically derive the generating Hamiltonians whose spectral properties determine the spectral form factor in the leading order. We further analyze the system-size $(L)$ scaling of Thouless time $t^*$, beyond which the spectral form factor follows the prediction of random matrix theory. The $L$-dependence of $t^*$ crosses over from $\log L$ to $L^2$ with an increasing Jaynes-Cummings mixing between qubits and fermions or bosons in a finite-sized chain, and it finally settles to $t^* \propto \mathcal{O}(L^2)$ in the thermodynamic limit for any mixing strength. The Rabi mixing between qubits and fermions leads to $t^*\propto \mathcal{O}(\log L)$, previously predicted for single species of qubits or fermions without total number conservation.